PeterDonis said:
The term "absolute simultaneity" already has a definition--you can't just decide to use your own instead of the standard one.
And what is the definition of absolute time ?
PeterDonis said:
The word "absolutely" is wrong. What "the entire edifice of relativity stands on" is that proper time is measured by (proper) clocks. But proper time is not "absolute"--it's just arc length along a timelike worldline. Such an arc length is invariant, yes--it's the same regardless of our choice of coordinates. But "invariant" is not "absolute". It's just "invariant".
Now you are just re-arranging words. Invariant means absolute, because everybody agree with such a quantity.
PeterDonis said:
The prediction of QM is quite clear: the measurements should commute. (Provided that the electrons are not allowed to interact further when they come back together--further interaction would change their joint quantum state.) Given the initial entanglement and no further interaction, the prediction for the measurement results is the same regardless of where in spacetime the measurement events are--they can be spacelike separated, timelike separated, null separated, or even the same event.
I was also under that impression. But the detector and the electron have space-like trajectories. And Bell didn't prove QM does not care, he proves the correlation is instantaneous. And there is only two "instantaneous" possible, the proper time of detector or the proper time of electrons... and entanglement is not a property of detector (and photon have zero proper time), so I happen to prefer the later possibility.
PeterDonis said:
A further comment: you seem to think that the proper time of the two electrons once they separate has something to do with determining the measurement results. It doesn't. Electron spin states are stationary, so they don't change with time; that means that, given the initial entanglement, it doesn't matter how much proper time elapses for each electron before a measurement on it is made. The QM prediction for the measurement results remains the same.
I know that. I think it
MAY be interesting to
perform an experiment to see if it's true.
I also think that having entangled state that do evolve with time would also be a quite interesting case. But from what you write, I guess those
cannot exist.
I like to args about logic possibility (that's why I like Bell's inequality). Correlation
is validated by experiments. Perfect correlation exist
only at space-time located event.
But you
may also think the wave function is
real, and that's where the information is stored "in limbo" waiting for detector to extract it "from there". Like this is also perfectly simulable by computer program. That's possibility one ... we live in a simulation.
The other more occam's like possibility is to
probe that. There
IS a connection between those spin orientation and space time. It occurs to me a long time ago that you could make the beam (of photon, that's easier) goes trough vast amount of twisted space (black matter, black hole sling shot), and then get them back to the same
place (and most probably not parallel). Then the instantaneous correlation is not even the most spooky thing. The spooky thing is the significance of
same angle.
Thus modifying your previous statement: "it
doesn't matter how much proper
time space elapses for each electron(photon) before a measurement on it is made". It is true ? If so how do you decide detector have the "same" angle ? (I wonder if a simple trip to the moon and back (or ricocheting between satellite) would not twisted the photon spin in some way)